ABCD and DCMK are squares. AB = 10 cm. O and P are the intersection points of the diagonals of squares ADCD and DCMK

ABCD and DCMK are squares. AB = 10 cm. O and P are the intersection points of the diagonals of squares ADCD and DCMK, respectively. Find the area of the OCPD quadrilateral.

Both squares have a common CD side, so both are the same and next to each other. Their diagonals form a new OCPD square, but smaller. The OC side of the square is half of the AC diagonal.
Find the diagonal AC:
AC = √ (AB ^ 2 + BC ^ 2) = √ (10 ^ 2 + 10 ^ 2) = 10 * √2 cm.
Find the side of the OCPD square:
OC = AC / 2 = 10 * √2 / 2 = 5√2 cm.
Let’s calculate the area of the square OCPD:
SOCPD = OC ^ 2 = (5√2) ^ 2 = 50 cm2.
Answer: area of the square  50 cm2.